A Hölder continuity result for a class of obstacle problems under non standard growth conditions

2011 ◽  
Vol 284 (11-12) ◽  
pp. 1404-1434 ◽  
Author(s):  
Michela Eleuteri ◽  
Jens Habermann
Keyword(s):  
Hölder Continuity ◽  
Growth Conditions ◽  
Obstacle Problems ◽  
Holder Continuity ◽  
Continuity Result

scholarly journals Weighted Hölder continuity of Riemann-Liouville fractional integrals – Application to regularity of solutions to fractional cauchy problems with Carathéodory dynamics

2019 ◽  
Vol 22 (3) ◽  
pp. 722-749 ◽  
Author(s):  
Loïc Bourdin
Keyword(s):  
Hölder Continuity ◽  
Fractional Integrals ◽  
Regularity Of Solutions ◽  
Cauchy Problems ◽  
Holder Continuity ◽  
Integrable Functions ◽  
Continuity Result

Abstract This paper is dedicated to several original (weighted) Hölder continuity results for Riemann-Liouville fractional integrals of weighted integrable functions. As an application, we prove a new weighted continuity result for solutions to nonlinear Riemann-Liouville fractional Cauchy problems with Carathéodory dynamics.

Hölder continuity up to the boundary for a class of fractional obstacle problems

2016 ◽  
Vol 27 (3) ◽  
pp. 355-367 ◽  
Author(s):  
Janne Korvenpää ◽  
Tuomo Kuusi ◽  
Giampiero Palatucci
Keyword(s):  
Hölder Continuity ◽  
Obstacle Problems ◽  
Holder Continuity

scholarly journals Global higher integrability for minimisers of convex functionals with (p,q)-growth

2021 ◽  
Vol 60 (2) ◽  
Author(s):  
Lukas Koch
Keyword(s):  
Hölder Continuity ◽  
Growth Conditions ◽  
Holder Continuity ◽  
Higher Integrability ◽  
Convex Functionals ◽  
Global Higher Integrability ◽  
Continuity Assumption

AbstractWe prove global $$W^{1,q}({\varOmega },{\mathbb {R}}^m)$$ W 1 , q ( Ω , R m ) -regularity for minimisers of convex functionals of the form $${\mathscr {F}}(u)=\int _{\varOmega } F(x,Du)\,{\mathrm{d}}x$$ F ( u ) = ∫ Ω F ( x , D u ) d x .$$W^{1,q}({\varOmega },{\mathbb {R}}^m)$$ W 1 , q ( Ω , R m ) regularity is also proven for minimisers of the associated relaxed functional. Our main assumptions on F(x, z) are a uniform $$\alpha $$ α -Hölder continuity assumption in x and controlled (p, q)-growth conditions in z with $$q<\frac{(n+\alpha )p}{n}$$ q < ( n + α ) p n .

scholarly journals Pointwise regularity for solutions of double obstacle problems on metric spaces

2011 ◽  
Vol 109 (2) ◽  
pp. 185 ◽  
Author(s):  
Zohra Farnana
Keyword(s):  
Metric Spaces ◽  
Hölder Continuity ◽  
Obstacle Problems ◽  
Holder Continuity ◽  
Hölder Continuous ◽  
Pointwise Regularity

We study continuity at a given point for solutions of double obstacle problems. We obtain pointwise continuity of the solutions for discontinuous obstacles. We also show Hölder continuity for solutions of the double obstacle problems if the obstacles are Hölder continuous.

\mathfrak{B}_{1} classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth

2019 ◽  
Vol 16 (3) ◽  
pp. 403-447
Author(s):  
Igor Skrypnik ◽  
Mykhailo Voitovych
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Hölder Continuity ◽  
Growth Conditions ◽  
Holder Continuity ◽  
Nonstandard Growth ◽  
Elliptic And Parabolic Equations ◽  
Functional Classes ◽  
Nonstandard Growth Conditions ◽  
Quasilinear Elliptic

The article provides an application of the generalized De Giorgi functional classes to the proof of the Hölder continuity of weak solutions to quasilinear elliptic and parabolic equations with nonstandard growth conditions.

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